Question: Is ${208416}$ divisible by $4$ ?
Solution: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{2084} {16} = \gray{2084} \gray{00} + {16} $ Because $208400$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${16}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $16$ , divisible by $4$ Yes, ${16 \div 4 = 4}$, so $208416$ must also be divisible by $4$.